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anastassius [24]

2 years ago

13

A right circular cylinder is changing shape. The radius is decreasing at the rate of 2 inches/sec while it's height is increasin

g at the rate of 5 inches/sec. When the radius is 4 inches and the height is 6 inches, how fast is the volume changing? Round your answer to three decimal places

1 answer:

Savatey [412]2 years ago

7 0

Answer:

<h3> 552.640in³/s</h3>

Step-by-step explanation:

Volume of a cylinder is expressed as;

$V = \pi r^2 h$

$\frac{dV}{dt} = \frac{dV}{dr} \frac{dr}{dt} +\frac{dV}{dh} \frac{dh}{dt}$

dV/dr = 2πrh

dV/dr = 2π(4)(6)

dV/dr = 48(3.14)

dV/dr = 150.72in³/m

dV/dh = πr²

dV/dh = 3.14(4)²

dV/dh = 50.24

Given

dh/dt = 5in/s

dr/dt = 2in/s

Substitute into the dV/dt

dV/dt = 150.72(2)+50.24(5)

dV/dt = 301.44 + 251.2

dV/dt= 552.640in³/s

The volume is changing at the rate of 552.640in³/s

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Twice the product of the cube of a and the square of b

arlik [135]

For this case we have to rewrite the given expression algebraically:

the cube of a, is represented as: $a ^ 3$

the square of b, is represented as: $b ^ 2$

Thus, the product of both expressions is:

$(a ^ 3 * b ^ 2)$

And twice the product is represented as:

$2 (a ^ 3 * b ^ 2)$

Answer:

$2 (a ^ 3 * b ^ 2)$

6 0

3 years ago

(6 x10^2) divided by (3 x 10^-5)<br> Give your answer in standard form.

alukav5142 [94]

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2 years ago

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valentina_108 [34]

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Step-by-step explanation:

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7 0

3 years ago

At a certain time of the day, a tree that is x meters tall casts a shadow that is x-49 meters long. If the distance from the top

nikklg [1K]

The height of the tree is 60 meters.

Explanation:

Let the height of the tree be x. The tree casts a shadow of $x-49$ meters and the distance from the top of the tree to the end of the shadow is $x+1$ meters.

The sides of the triangle are attached in the image below:

Using pythagoras theorem,

$x^{2}+(x-49)^{2}=(x+1)^{2}$

Expanding, we get,

$2 x^{2}-98 x+2401=x^{2}+2 x+1$

$2 x^{2}-98 x+2400=x^{2}+2 x$

$2 x^{2}-100 x+2400=x^{2}$

$x^{2}-100 x+2400=0$

Solving the equation using the quadratic formula $x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$ , we get,

$x=\frac{-(-100)\pm\sqrt{(-100)^{2}-4 \cdot 1 \cdot 2400}}{2 \cdot 1}$

Simplifying, we have,

$x=\frac{100\pm\sqrt{10000-9600}}{2}$

$x=\frac{100\pm\sqrt{400}}{2}$

$x=\frac{100\pm{20}}{2}$

Thus,

$x=\frac{100+20}{2} \\x=\frac{120}{2} \\x=60$ and $x=\frac{100-20}{2} \\x=\frac{80}{2} \\x=40$

where the value $x=40$ is not possible because substituting the value $x=40$ in $x-49$ results in negative solution. Which is not possible.

Hence, the value of x is 60.

Thus, The height of the tree is 60 meters.

7 0

3 years ago

There are 200 pieces of gum. The first student gets one-half and each student gets half of what's left each time. How many piece

grin007 [14]

Answer: the 7th person will get 3.125 pieces of gum.

Step-by-step explanation:

The first student gets one-half and each student gets half of what's left each time. This means that number of pieces of gum that each student gets is reducing in geometric progression. The formula for determining the nth term of a geometric progression is expressed as

Tn = ar^(n - 1)

Where

a represents the first term of the sequence.

r represents the common ratio.

n represents the number of terms.

From the information given,

a = 200

r = 0.5

n = 7

The 7th term, T7 is

T7 = 200 × 0.5^(7 - 1)

T7 = 200 × 0.5^6

T7 = 3.125

7 0

3 years ago